Hybrid Unet-Transformer Model for Generating Stress and Strain Fields from Composite Geometrics

Accurate prediction of stress and strain fields in hierarchical composite microstructures is critical for physics-informed material design, yet conventional finite element method (FEM) simulations are computationally prohibitive at scale, requiring minutes to days per evaluation. In this work, we propose a hybrid UNet-Transformer architecture that predicts complex mechanical field distributions directly from composite microstructure geometry images, serving as an efficient surrogate for FEM across ten distinct stress and strain field types spanning diverse two-phase composite configurations including square, hexagonal, and triangular tessellations, multiple boundary conditions, and high-resolution geometries. Results demonstrate that the proposed architecture achieves strong predictive performance across the majority of subdatasets, with peak accuracy on periodic tessellation geometries reaching R2=0.9991, SSIM=0.9936, and MAE=0.0050 on the boundary condition subdataset and the triangular tessellation subdataset respectively. Across six of the eight evaluated subdatasets, MAE remains below 0.05 on the normalized [0,1] pixel scale. Encoder attention analysis via Grad-CAM and Grad-CAM++ confirms that the model develops physically meaningful internal representations, localizing attention at mechanically critical regions including phase boundaries, ligament junctions, and indenter contact zones without explicit structural supervision. Performance degrades on irregular square-grid geometries with sparse soft-phase inclusions, with the S11 normal stress subdataset yielding R2=0.7735 and SSIM=0.7126, consistent with the known limitation of smooth-loss image translation models in reproducing sharp stress discontinuities.

Multi-fidelity surrogates for mechanics of composites: from co-kriging to multi-fidelity neural networks

Composite materials exhibit strongly hierarchical and anisotropic properties governed by coupled mechanisms spanning constituents, plies, laminates, structures, and manufacturing history. This intrinsic complexity makes predictive modeling of composites expensive, because repeated experiments and high-fidelity simulations are needed to cover large design spaces of material, structure, and manufacturing. Multi-fidelity surrogate modeling addresses this challenge by combining abundant, less expensive data with limited high-accuracy data to recover reliable high-fidelity predictions. This review presents a structured overview of multi-fidelity modeling for composite mechanics, covering Gaussian-process or Kriging-based methods, including co-Kriging, coregionalization models, autoregressive formulations, nonlinear autoregressive Gaussian processes, multi-fidelity deep Gaussian processes, and multi-fidelity neural networks. Their distinctions are examined in terms of cross-fidelity correlation, discrepancy representation, uncertainty quantification, and scalability. Selected examples of their applications to composites are introduced according to the roles that multi-fidelity surrogates play in engineering problems, including forward prediction for rapid exploration of material design spaces, inverse optimization for composite parameter identification and design search under limited high-fidelity access, and workflow integration, where heterogeneous data sources, constraints, and validation requirements determine model utility. Open question discussions highlight recurring challenges specific to composites, such as regime-dependent fidelity gaps associated with nonlinear damage and manufacturing history, mismatches between simulations and experiments, and uncertainty propagation across multi-fidelity models.